Detail publikace

# New algorithm of numerical inversion of D-transform

BIOLEK, D. BIOLKOVÁ, V. KOLKA, Z.

Originální název

New algorithm of numerical inversion of D-transform

Anglický název

New algorithm of numerical inversion of D-transform

Jazyk

en

Originální abstrakt

The D-transform, introduced in 1998 by J. Hekrdla, converts a continuous-time signal to a sequence. In contrast to the classical sampling, there is no such visible connectivity between the continuous-time signal and its discrete-time counterpart in the time domain. The main feature of the D-transform consists in preserving the relations between the derivative of continuous-time signal and the difference of discrete-time signal. This fact enables, among other things, changing the problem of numerical solution of differential equations into the simpler problem of solving difference equations, without losing accuracy. The inverse D-transform represents a pending issue because it cannot be derived in closed form as in the case of the Fourier, Laplace, or other known transforms. This paper describes a novel method of D-transform inversion, which is based on mutual correspondence between the D-, z-, and Laplace transforms. Numerical accuracy is provided by the algorithm of the inverse Laplace transform, which works reliably also in the case of periodical or divergent signals.

Anglický abstrakt

The D-transform, introduced in 1998 by J. Hekrdla, converts a continuous-time signal to a sequence. In contrast to the classical sampling, there is no such visible connectivity between the continuous-time signal and its discrete-time counterpart in the time domain. The main feature of the D-transform consists in preserving the relations between the derivative of continuous-time signal and the difference of discrete-time signal. This fact enables, among other things, changing the problem of numerical solution of differential equations into the simpler problem of solving difference equations, without losing accuracy. The inverse D-transform represents a pending issue because it cannot be derived in closed form as in the case of the Fourier, Laplace, or other known transforms. This paper describes a novel method of D-transform inversion, which is based on mutual correspondence between the D-, z-, and Laplace transforms. Numerical accuracy is provided by the algorithm of the inverse Laplace transform, which works reliably also in the case of periodical or divergent signals.

Dokumenty

BibTex

``````
@article{BUT43780,
author="Dalibor {Biolek} and Viera {Biolková} and Zdeněk {Kolka}",
title="New algorithm of numerical inversion of D-transform",
annote="The D-transform, introduced in 1998 by J. Hekrdla, converts a continuous-time signal to a sequence. In contrast to the classical sampling, there is no such visible connectivity between the continuous-time signal and its discrete-time counterpart in the time domain. The main feature of the D-transform consists in preserving the relations between the derivative of continuous-time signal and the difference of discrete-time signal. This fact enables, among other things, changing the problem of numerical solution of differential equations into the simpler problem of solving difference equations, without losing accuracy. The inverse D-transform represents a pending issue because it cannot be derived in closed form as in the case of the Fourier, Laplace, or other known transforms. This paper describes a novel method of D-transform inversion, which is based on mutual correspondence between the D-, z-, and Laplace transforms. Numerical accuracy is provided by the algorithm of the inverse Laplace transform, which works reliably also in the case of periodical or divergent signals.",